Question

Draw the graph of each of the following linear equations in two variables:6x-2y=7

Answer 1

Answer:

matee I have different solutions but the steps are same you can understand the sequence and solve and I don't know about graph -n-"

Step-by-step explanation:

Given 6x−3y=12

⟹3(2x−y)=12

⟹2x−y=4

⟹y=2x−4⋯(1)

To draw the graph , we need atleast two solutions

Also to find the coordinates of the points where the graph cuts the coordinate axes,put x=0 and y=0 respectively

Put x=0 in (1)

⟹y=2(0)−4=0−4=−4

(0,−4) is the solution of given line

Put y=0

⟹0=2x−4

⟹2x=4

⟹x=2

(2,0) is the solution of given line

With these two solutions we can draw graph of 6x−3y=12

(2,0) & (0,−4) are the points where the graph cuts the coordinate axes

Hope it helps you

Answer 2

$\large\underline{\sf{Solution-}}$

Given linear equation is

$\rm :\longmapsto\:6x - 2y = 7$

can be rewritten as

$\rm :\longmapsto\:2y = 6x - 7$

On substituting x = 0, we get

$\rm :\longmapsto\:2y = 6(0) - 7$

$\rm :\longmapsto\:2y = - 7$

$\bf\implies \:y = - 3.5$

Now,

On substituting x = 1, we get

$\red{\rm :\longmapsto\:2y = 6(1) - 7}$

$\red{\rm :\longmapsto\:2y = 6 - 7}$

$\red{\rm :\longmapsto\:2y = - 1}$

$\red{\bf\implies \:y = - 0.5}$

Now,

On substituting x = 2, we get

$\green{\rm :\longmapsto\:2y = 6(2) - 7}$

$\green{\rm :\longmapsto\:2y = 12 - 7}$

$\green{\rm :\longmapsto\:2y = 5}$

$\green{\bf\implies \:y = 2.5}$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\purple{\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 3.5 \\ \\ \sf 1 & \sf - 0.5 \\ \\ \sf 2 & \sf 2.5 \end{array}} \\ \end{gathered}}$

➢ Now draw a graph using the points

➢ See the attachment graph.